I did my first "real" deadlift today, and, it's a very different feeling. Unlike a squat or a bench, where I clearly feel myself pushing against something, when I deadlifted (135 lbs, about what I'm squatting), I just kind of stood up. When I was done, I was sweating and exhausted, but I didn't feel the push-higher-higher I do when doing other lifts.

You didn't feel like you were pushing anything because you weren't. You're holding on to something and standing up. Most of the time a heavy deadlift feels to me like squeezing everything tight, locking it in place, and standing up.

Once you get real heavy--one and a half times bodyweight, probably, but your mileage may vary--you'll feel a "higher-higher-higher-come-on-stand-up" feeling. Right now you're not close enough to your maximum to get that.

I don't know if it's "supposed" to feel like anything in particular, but it may take some time to develop the mind/muscle connection if you're unused to specifically activating the deadlift muscles.

It also matters which style of deadlift you're doing, for example, there are differences between stiff-legged deadlifts (erectors, hips, butt, some thighs) and "traditional" deadlifts (same plus a bunch more, great overall exercise).

You'll also want to make sure your form is pretty dead-(lift)on, you're "blocking" appropriately, and so on. Having someone to work with when doing an exercise like the deadlift is pretty important since the risk of a back injury is greater than with a lot of other exercises--slipping a disk is unpleasant, I'm told.

That you're ending up feeling pretty worked leads me to believe you're doing "traditional" deadlifts. Since it's an-almost-entire-body exercise, you won't necessarily feel the "I'm working this specific muscle" feeling you get from more-targeted movements like the bench or squat.